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      OpenFOAM-3.0 的湍流模型（一）
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        <p>本系列分析 OpenFOAM-3.0 版本的湍流模型。从 3.0 版开始，OpenFOAM 中的湍流模型架构发生了较大的变化，其实这种变化在 2.3 版开始已经初露端倪，在 2.3 版里，多相流的湍流模型已经开始跟单相流湍流模型分开。从 3.0 开始，单相流湍流模型和多相流湍流模型统一到了一个架构下。本系列将对 3.0 版的湍流模型进行详细的分析，分为四部分：结构概览，RTS 机制分析，编译新模型的方法，以及一些补充说明。</p>
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<h5 id="1-_结构概览">　1.  结构概览</h5><p>这部分主要是概括一下湍流模型的框架的结构，如下图（请点击右键查看大图）：</p>
<p><img src="/image/turbulenceModel/turbulenceModel-3.0.png" alt="湍流模型的架构"></p>
<p>图片中，蓝色字体的是类名，绿框中的类是调用 <code>declareRunTimeSeclectionTable</code> 的类（如果对这个的含义感兴趣，建议参考<a href="http://xiaopingqiu.github.io/2016/03/12/RTS1/" target="_blank" rel="external">这篇</a>或者<a href="http://www.sourceflux.de/blog/run-time-type-selection-openfoam-selecting-types-based-type-name/" target="_blank" rel="external">这篇</a>），四种不同颜色的箭头，代表的是四种不同的湍流模型：单相不可压缩湍流模型，单相可压缩湍流模型，多相不可压缩模型，多相可压缩模型。</p>
<p>在图片下面，我用了一个 <code>kEpsilon</code> 和一个 <code>Smagorinsky</code> 模型作为示例，这是因为，这两个湍流模型都是以通用形式来实现的，从 C++ 角度来说，就是模板类。通过代入不同的模板参数， <code>kEpsilon</code> 和 <code>Smagorinsky</code> 这两个模板类可以实例化为不同种类的湍流模型。<br><figure class="highlight haskell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br></pre></td><td class="code"><pre><span class="line"><span class="title">template</span>&lt;<span class="keyword">class</span> <span class="type">BasicTurbulenceModel</span>&gt;</span><br><span class="line"><span class="class"><span class="keyword">class</span> kEpsilon</span><br><span class="line">:</span><br><span class="line">    public eddyViscosity&lt;<span class="type">RASModel</span>&lt;<span class="type">BasicTurbulenceModel</span>&gt; &gt;</span><br><span class="line">&#123;</span><br><span class="line">    // <span class="type">Private</span> <span class="type">Member</span> <span class="type">Functions</span></span><br><span class="line"></span><br><span class="line">        // <span class="type">Disallow</span> default bitwise copy construct and assignment</span><br><span class="line">        kEpsilon<span class="container">(<span class="title">const</span> <span class="title">kEpsilon</span>&amp;)</span>;</span><br><span class="line">        kEpsilon&amp; operator=<span class="container">(<span class="title">const</span> <span class="title">kEpsilon</span>&amp;)</span>;</span><br><span class="line"></span><br><span class="line">	......</span><br><span class="line">	......</span><br><span class="line"></span><br><span class="line"> tmp&lt;fvScalarMatrix&gt; epsEqn</span><br><span class="line">    <span class="container">(</span><br><span class="line">        <span class="title">fvm</span>::<span class="title">ddt</span>(<span class="title">alpha</span>, <span class="title">rho</span>, <span class="title">epsilon_</span>)</span></span><br><span class="line">      + fvm::div<span class="container">(<span class="title">alphaRhoPhi</span>, <span class="title">epsilon_</span>)</span></span><br><span class="line">      - fvm::laplacian<span class="container">(<span class="title">alpha</span>*<span class="title">rho</span>*<span class="type">DepsilonEff</span>()</span>, epsilon_)</span><br><span class="line">     ==</span><br><span class="line">        <span class="type">C1_</span>*alpha*rho*<span class="type">G</span>*epsilon_/k_</span><br><span class="line">      - fvm::<span class="type">SuSp</span><span class="container">(((2.0/3.0)</span>*<span class="type">C1_</span> + <span class="type">C3_</span>)*alpha*rho*divU, epsilon_)</span><br><span class="line">      - fvm::<span class="type">Sp</span><span class="container">(<span class="type">C2_</span>*<span class="title">alpha</span>*<span class="title">rho</span>*<span class="title">epsilon_</span>/<span class="title">k_</span>, <span class="title">epsilon_</span>)</span></span><br><span class="line">      + epsilonSource<span class="container">()</span></span><br><span class="line">      + fvOptions<span class="container">(<span class="title">alpha</span>, <span class="title">rho</span>, <span class="title">epsilon_</span>)</span></span><br><span class="line">    );</span><br><span class="line"></span><br><span class="line">    epsEqn<span class="container">()</span>.relax<span class="container">()</span>;</span><br><span class="line">    fvOptions.constrain<span class="container">(<span class="title">epsEqn</span>()</span>);</span><br><span class="line">    epsEqn<span class="container">()</span>.boundaryManipulate<span class="container">(<span class="title">epsilon_</span>.<span class="title">boundaryField</span>()</span>);</span><br><span class="line">    solve<span class="container">(<span class="title">epsEqn</span>)</span>;</span><br><span class="line">    fvOptions.correct<span class="container">(<span class="title">epsilon_</span>)</span>;</span><br><span class="line">    bound<span class="container">(<span class="title">epsilon_</span>, <span class="title">this</span>-&gt;<span class="title">epsilonMin_</span>)</span>;</span><br><span class="line"></span><br><span class="line">    // <span class="type">Turbulent</span> kinetic energy equation</span><br><span class="line">    tmp&lt;fvScalarMatrix&gt; kEqn</span><br><span class="line">    <span class="container">(</span><br><span class="line">        <span class="title">fvm</span>::<span class="title">ddt</span>(<span class="title">alpha</span>, <span class="title">rho</span>, <span class="title">k_</span>)</span></span><br><span class="line">      + fvm::div<span class="container">(<span class="title">alphaRhoPhi</span>, <span class="title">k_</span>)</span></span><br><span class="line">      - fvm::laplacian<span class="container">(<span class="title">alpha</span>*<span class="title">rho</span>*<span class="type">DkEff</span>()</span>, k_)</span><br><span class="line">     ==</span><br><span class="line">        alpha*rho*<span class="type">G</span></span><br><span class="line">      - fvm::<span class="type">SuSp</span><span class="container">((2.0/3.0)</span>*alpha*rho*divU, k_)</span><br><span class="line">      - fvm::<span class="type">Sp</span><span class="container">(<span class="title">alpha</span>*<span class="title">rho</span>*<span class="title">epsilon_</span>/<span class="title">k_</span>, <span class="title">k_</span>)</span></span><br><span class="line">      + kSource<span class="container">()</span></span><br><span class="line">      + fvOptions<span class="container">(<span class="title">alpha</span>, <span class="title">rho</span>, <span class="title">k_</span>)</span></span><br><span class="line">    );</span></span><br></pre></td></tr></table></figure></p>
<p>从上述代码可以看出，输运方程中带入了密度 <code>rho</code> 和代表相体积分率的 <code>alpha</code> 。代入不同的模板参数， <code>rho</code> 和 <code>alpha</code> 的取值也会不同，从而实例化为不同的湍流模型，详细的后文还会分析。除此之外，输运方程中还加入了两种源项的实现，一种是以成员函数的形式（ <code>epsilonSource()</code> 和 <code>kEpsilon()</code> ）；另一种是以 <code>fvOptions</code> 的形式，允许用户自定义源项。</p>
<p>在这个架构下，湍流模型是怎么通过 RTS 机制来进行选择的呢？请看下一篇。</p>

      
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